3 SECTORAL DESCRIPTION (10) [Equations are included in
3.5 Income Distribution .1 CANDIDE 2.0
The income side of the CANDIDE model with the exception of the wage bill is not disaggregated by industry. However, the individual components are generally modelled. Capital consumption allowances is determined by a rate base calculation on the capital stock. Income of non-farm
unincorporated business is influenced by the current dollar value of imputed and paid rent and the unemployment rate. Farm income is dependent on farm production and prices. Interest and miscellaneous investment income is determined by an add-up of the components. Once the components of net national income are determined, profits are derived residually. Since profits are the residual and since wages respond with a lag to shocks, profits fluctuate proportionately the most in response to changes in interest rates, inflation and output.
3.5.2 TIM
GDP is derived in TIM by adding to GNP, the residual error of the estimate and subtracting net indirect taxes and subsidies and net foreign receipts. The components of GDP are disaggregated as the sum of factor incomes including labour income, return to capital, capital consumption allowance and income from unincorporated business. The national accounts definitions of incomes are also modelled. As in CANDIDE corporate profits are treated as a residual.
3.5.3 RDX2
Behavioural equations are found in RDX2 for some income components including dividends and net income of non-farm unincorporated business including rent. Interest income, however, is exogenous. The original version of RDX2 had an equation for corporate profits before tax as a function of three explanatory variables approximating charges for the use of capital, sales plus inventory accumulation, and the cost of labour. In the original version the discrepancy between total national accounts expenditure and income was treated as an endogenous variable and
included in personal income for simulations. In the latest version of RDX2 corporate profits are a residual.
3.5.4 CHASE
In the CHASE model, except for wages, IVA, and capital consumption allowances, private sector income components are modelled as shares. The wage bill is calculated from wages and
employment. The change in capital consumption allowances depends on nominal investment.
Corporate profits are the income side residual.
3.5.5 DRI
DRI has equations for interest income, dividends, capital consumption allowances, and corporate profits. Corporate profits as a proportion of GNP are a function of prices, wages as a share of GNP, and capacity utilization. The income side residual in the DRI model is the income of non-farm unincorporated business including rent. It is defined as national income less all other components of income and is included in personal income.
3.5.6 FOCUS
FOCUS has equations for interest income and dividends paid to non-residents. It also has equations for corporate profits, IVA and capital consumption allowances. Corporate profits as a share of total property income are inversely related to the unemployment rate and directly related to the rate of capacity utilization, the ratio of real final goods sales to real private GNP and the ratio of non-energy merchandise exports to private GNP in current prices. The income-side residual in FOCUS as in the DRI model is the income of unincorporated business including rent. This reflects the common descent of the FOCUS and DRI models from the earlier University of Toronto Quarterly Forecasting Model (QFM).
3.5.7 MTFM
MTFM has stochastic equations for many of the private sector income side components in addition to determining the wage bill using industry equations for wages and employment. The components modelled include: business CCA, non-farm unincorporated business,
IVA, interest and miscellaneous investment income of persons. The equation for the latter explicitly incorporates financial asset stocks. Corporate profits are determined residually.
3.5.8 QFS
The various components on non-wage net national income are modelled as functions of related GNE and financial variables. Corporate profits are a function of unit labour costs, real final domestic demand, the final domestic demand deflator and real exports. The equation is specified as a first difference in the current value of the LHS and RHS variables divided by the lagged variables. The equation is also corrected forautocorrelation. The income expenditure residual is allocatedacross components in relation to their respective shares of non-wage net national income.
3.5.9 RDXF
RDXF has stochastic equations for most important private sector income components. These include: accrued net income of farm operators from farm production; miscellaneous personal investment income; net income of non-farm unincorporated business; and capital consumption allowances. The equation for corporate profits is specified as a proportion of GNP and includes asset stocks, interest rates, the exchange rate, and various income and expenditure components. It also includes a variable which is the sum of corporate profits before tax, miscellaneous personal investment income, and the net income of non-farm unincorporated business including rent. This variable, which can also be viewed as the income side residual, is spread amongst its three
components in simulations so that the income and expenditure side of the national accounts balance.
3.5.10 MACE
MACE only has a very rudimentary income sector. All components are not specified and there is no income side add-up. Items that are treated explicitly are the wage bill and capital consumption allowances. Indirect taxes are also modelled. Corporate profits are not defined in MACE.
3.5.11SAM
SAM has a highly aggregated income sector. Income is split between the wage bill, gross profits, payments to energy, and indirect taxes. Business profits are technically a residual and
thus reflect disequilibrium factor payments as excess profits. Profits feed through to the asset sector as the return on equity. Because of the highly aggregated nature of the income
distribution, the SAM measure of profits is not identical to the national accounts measure of corporate profits, but includes other business income components not treated separately.
3.6 Housing
3.6.1 CANDIDE 2.0
The CANDIDE 2.0 housing block includes: 1) expenditure on single housing units; 2) expenditure on multiple housing units; 3) expenditure on mobile homes; 4) expenditures on cottages; and 5)
expenditures on real estate commissions and; 6) an "other" category.
The key single and multiple housing starts equations are a function of new residential mortgage approvals, demographic factors, the relative advantage of renting versus owning, a proxy
for the lagged change in vacancies, and dummy variables for government policies such as winter works programs and the deductibility of capital consumption allowances from other income.
The single housing starts (RSS) equation is:
(1)
RSS = 128.54600 + .019894 * (FMAP.PNRWRT + FMAP.CMHC.SD)/PFRCINAB (2)
+ .0081887 * (FMAP.PNWRTC(-1) + FMAP.CMHC.SD(-1))/PFRCINAB(-1) (3)
+ 5.29181 * RDUMWW (4)
+ 119.69400 * (PFHOWIX/PFCSR20) (5)
+ .72398 * J1D(DMPOP30.34 + DFPOP30.34)
where the first (1) and second (2) terms are the value of private and CMHC mortgage approvals deflated by the residential
construction deflator, RDUMWW is the winter works dummy, the fourth (4) term represents the cost of home ownership relative to renting, and the fifth (5) term is the change in the population between age 30 and 34.
The multiple housing starts (RMS) equation is:
(1)
RMS = 8.29247 + .023538 * (FMAP.PNWRT + FMAP.CMHC.MD)/PFRCINAB (2)
+ .0043858 * (FMAP.PNWRT(-1) + FMAP.CMHC.MD)/PFRCINAB(-1) (3)
+ 22.71000 * RDRCCAIP(-1) (4)
- .19724 * (RMS(-2) - J1D(DMPOP20.24(-2) + DMPOP25.29(-2))) + DFPOP20.24(-2) + DFPOP25.29(-2))
+ .12700 * J1D(DMPOP20.24 + DMPOP25.29 + DFPOP20.24 + DFPOP25.29) where terms (1) and (2) are real mortgage approvals, RDRCCAIP is
the capital consumption allowance dummy variable, term (4) is the difference between lagged multiple starts and the change in the number of young people age 20 to 29, the latter being a proxy for demographic demand, which is also entered separately as term (5).
Completions and expenditures on residential construction are explained as a lag on single and multiple housing starts. Expenditure also includes real estate commissions, which are
explained by a rate-base equation, and an other category, which is influenced by real disposable income and completions.
The major impact of financial variables on housing functions through the mortgage
approval-mortgage assets channel. The mortgage approvals of insurance companies, trust and mortgage companies, and chartered banks are determined by their earning
assets and interest rates on mortgages and competing assets.
3.6.2 TIM
The TIM housing sector explains both single and multiple housing starts. Two simplifying assumptions are made: 1) families prefer single units, and 2) single people live in multiple units.
The equation for single starts (HSS) is:
HSS = a0 + a1 * (.75 * PFES - PFESRR) * FAMHO + a2 * REALI where PFES is the percentage of families eligible for single
units (this is a function of disposable income per household divided by the average mortgage payment), PFESRR is the percentage of families estimated to be already in singles, FAMHO is family households, and REALI is the real interest rates defined as yield on commercial paper minus the percentage change in the GNE deflator.
The equation for multiple starts (HMS) is:
HMS = b0 + b1 * ((PFEM - PFEMRR) * FAMHO) + b2 * J1D(NFHO) + b3 * (CANPCP - J1P(CSR2OP))
where PFEM is the percentage of families eligible for multiple units (this is a five year distributed lag on disposable income per household divided by the average mortgage payment), PFEMRR is the percentage of families estimated to already be residing in multiple units, FAMHO is the
number of family households, NFHO is the number of
non-family households, CANPCP is the commercial paper rate, and CSR2OP is the price deflator for paid space rent.
The average mortgage payment used in calculating the percentage of families eligible for the units is a function of interest rates, land costs and house costs.
Completions and expenditures are derived as distributed lags on starts. Expenditures also incorporate: expenditures on conversions which are exogenous; alterations and additions, which depend on disposable income and the housing stock; and supplementary costs of new housing which are tied to housing starts.
3.6.3 RDX2
The original version of RDX2 explained housing starts in a reduced form equation incorporating real disposable income per household and credit conditions. In the latest version of RDX2 housing starts are tied directly to mortgage loans by a technical relationship to reflect the fact that most residential construction is financed by mortgage loans. The equation for housing starts was specified:
(14.765 * HSTS + 9.843 * HSTM) = -211.62 * (1-ZWW) * QC1 + 91.913 * (1-ZWW) * QC2 + 84.562 * (1-ZWW) * QC3 + 151.49 * (1-ZWW) + 100.84 * ZWW - 183.36 + ZWW * QC1 + 20.500 * ZWW * QC2 + 83.284 * ZWW * QC3
+ JW((HAPNRESD + HAPCMHCS + HAPCMHCM +HAPNROT)/PIRC) where ZWW is a dummy variable for winter works equal to 1 from
63Q3 to 66Q2, QC1, QC2, and QC3 are quarterly dummy variables, HAPNRESD is mortgage approvals for new residential construction by life insurance, trust, and mortgage and loan companies, and chartered banks,
HAPCMHCS is direct CMHC loans for singles, HAPCMHCM is direct CMHC loans for multiples, HAPNROT is mortgage approvals by other lenders, and PIRC is the deflator
for residential construction.
The constants 14.765 and 9.843 are the average cost for a single and multiple unit under the National Housing Act in 1961. These constants translate starts into dollars. The sum of the weights on mortgage approvals is 1.07184. This is very close to the value of 1 which would occur if all units were totally financed by mortgages.
The housing starts equation was solved for single units and the number of multiple units was simultaneously determined on the basis of an exogenous split.
To understand how interest rates impact on housing starts it is necessary to go beyond the housing start equation into the determination of mortgage interest rates and mortgage approvals.
There are two main ways that an increase in interest rates would affect housing starts in RDX2.
First, higher interest rates would reduce the total assets of mortgage lenders. Second, as interest rates went up, the gap between the conventional mortgage rate and the average yield on 3 to 5 year government bonds would narrow, thus encouraging trust companies and banks to devote a smaller share of their assets to mortgage lending. This would cause housing starts to decrease.
The equations for mortgage approvals can be viewed as supply of funds equations. The key demand equation is for the conventional mortgage rate to which the bank and NHA mortgage rates are tied. The conventional mortgage rate responds with a Koyck lag negatively to real housing approvals per household and the stock of housing per household and positively to the long-term government bond rate and permanent income.
Expenditure on residential construction is composed of new housing expenditures, alterations, and supplementary housing stock costs. Expenditure on new housing depends on lagged housing starts. Other expenditures on residential construction is modelled as a function of the lagged housing stock.
3.6.4 CHASE
The CHASE model has one stochastic equation for housing starts. The split between singles and multiples is done using an exogenous ratio.
The key starts equation incorporates both demand and supply elements and is as follows.
(1)
LOG(HSCA/NPOPCA) = 5.78950 + 2.17797 * LOG(YRPPCA/NPOPCA) (2)
- 3.45260 * LOG(KRESDCA/NPOPCA) (3)
- .06065 * RMTCCA + .17977 * DUMMY (4)
+ .34756 * LOG(PMLSCA/PHCCA)
where HSCA is total housing starts, YRPPCA is real effective purchasing power in 1971 dollars, NPOPCA is the
non-institutional population 15 years and over, KRESDCA is the stock of houses in 1971 dollars,
RMTCA is the conventional mortgage rate, DUMMY is a dummy variable equal to 1 in 78Q1 and -1 in 78Q2, PMLSCA is the
price of multiple listing service houses, and PHCCA is construction cost per unit for single detached units.
Term (1) captures the impact of real purchasing power per capita on housing demand, Term (3) indicates the negative impact of mortgage interest rates on housing demand. Terms (1) and (3) together could be viewed as giving the desired stock of housing per capita. Term (2) reflects the housing stock per capita. The difference between the sum of terms (1) and (3) and term (2) could be interpreted as the gap between actual and desired housing demand. Term (4) introduces a supply element. The ratio of the multiple listing price to construction costs is an indicator of the profitability of housing construction to developers.
The key price equation for housing is that for multiple listing service houses. It is a demand price modelled by inverting a demand for housing function. Its specific functional form is:
(1)
LOG(PMLSCA/PCICA) = -.09271 + 1.03247 * LOG(YRPCCA/NPOPCA) (2)
+ .59892 * LOG(PMLSCA(-1)/PCICA(-1)) (3)
- .0010763 * (RMTCA -J1P(PMLSCA(-1)) (4)
- .61558 * LOG(KRESDCA/NPOPCA)
where all variables are as defined above with the addition of PCICA which is the consumer price index.
Term (1) is the real effective purchasing power per capita and reflects demand as does term (3) which is the real mortgage rate. Term (4) represents the lagged stock of housing per capita. The difference between the sum of the terms (1) and (3) and term (4) is an indicator of the
disequilibrium between demand and supply. Term (2) is the lagged left hand side variable and allows for lagged adjustment.
The other key variable in the housing sector is construction cost per unit for single detached dwellings. It is a function of labour costs, energy prices, and total factor productivity in construction. Construction costs per unit is a supply price that enters in the housing starts
equation as the ratio of the demand price to the supply price, measuring the profitability of home building.
Expenditure on residential construction depends on lagged housing starts. An exogenous scaling ratio relating total investment in residential construction to new housing is utilized to allow for other residential construction expenditures.
3.6.5 DRI
The main housing start equation in the DRI model is a reduced form for total starts incorporating demand and supply elements. Its general form is:
(1)
HUSTDRI = f((YD,RMMTGNS,PICR71), KHOUS(-1), CPI@@CSRENT&/CPI, "CREDIT71", DMYMURB, DMYEXP) * N15
where HUSTDRI is additively adjusted total housing starts, YD is nominal disposable income, RMMTGNS is the mortgage rate, KHOUS is the stock of housing, CPI@@CSRENT&/CPI is the relative rental income as proxied by the consumer price
index for rental income to the all items index,
"CREDIT71" is the deflated sum of personal savings deposits and non-personal term and notice deposits at chartered banks, DMYMURB captures the impact of MURBs on housing starts, DMYEXP is included to reflect the crowding out impact of Expo 67 on housing, and N15 is the population over 15.
Term (1) represents the burden of homeownership as proxied by a function of disposable income, mortgage rates, and the costs of new housing.
Another equation explains the proportion of multiples to total housing starts (HUST2&%). It is of the form:
HUST2&% = f(CPI@@CSRENT&/CPI, YD71/N15, DMYMURB, DMYMURB814), N15/(N - N15&))
where YD71 is real disposable income, DMYMURB814 allows for the cancellation of MURBs in the November 1981 budget,
NR15& is the 15 and over population, and (N - N15&) is the under 15 population.
It is thus a function of the rental income proxy, per capita real disposable income. The function is homogenous of degree one with respect to the ratio of the 15-and-over population to the
under-15 population.
Single starts are explained from the housing starts identity. Completions and expenditures on residential construction are lagged functions of housing starts. The equation for expenditures on residential construction also includes a housing stock term tom proxy renovation/repair
expenditures and real estate commissions paid on resales of the existing housing stock.
3.6.6 FOCUS
The housing sector of the FOCUS model is patterned on that of RDX2. According to the RDX2 specification housing starts are driven by real mortgage approvals. An important difference between FOCUS and RDX2 is that in FOCUS separate equations exist for both single and multiple starts instead of a single equation for weighted starts.
The equation for single housing starts (HUST1NS) is:
HUSTS1NS = 15.7674 + (ai * constrained seasonal dummies
* (1 - DUMWWORKS) + (bi * constrained seasonal dummies * DUMWWORKS) - 1.0993 * DUMWORKS
+ JW((APPLMTGNWRPRIVNS + APPLMTGNWRCMHCNS)/PICR71VR) + JW(DUMTAXREFORM * (APPLMTGNWRPRIVNS
+ APPLMTGNWRCMHCNS)/PICR71VR)
where DUMWWORKS is a dummy variable for winter works in the 1960s, APPLMTGNWRPRIVNS is mortgage approvals by private sources such as banks, life insurance companies, trust and mortgage
and loan companies and others, APPLMTGNWRCMHCNS is approvals for new construction by CMHC, PIC71VR is the implicit price deflator for residential construction, and
DUMTAXREFORM is a dummy variable representing the impact of tax reform and the exception of owner occupied housing from capital gains in increasing the demand for housing.
The equation for multiple units (HUST2&NS) is similarly specified:
HUSTS2&NS = -6.19528 + (ai * constrained seasonal dummies * (1 - DUMWWORKS)
+ (bi * constrained seasonal dummies * DUMWWORKS) - 2.8131 * DUMWWORKS
- JW((APPLMTGNWRPRIVNS + APPLMTGNWRCMHCNS/PIC71VR) + JW((DUMTAXREFORM * (APPLMTGNWRPRIVNS
+ APPLMTGNWRCMHCNS/PICR71VR)
The sum of the coefficients on mortgage approvals for single and multiple starts indicates that since tax reform an additional $1 million in approvals has financed 19.5 single starts and 46 multiple starts.
Mortgage approvals by private lending institutions is a function of total mortgage approvals by the individual category of lending institution. The proportion of lending allocated to residential mortgages responds negatively to an aggregate vacancy rate and to the level of non-residential construction and CMHC approvals. The mortgage approvals of individual categories of financial institutions are influenced by such variables as permanent income and mortgage and other
interest rates. Some of these influences work indirectly through their impact on the total assets of the
lending institutions. Institutional aspects of mortgage lending are also taken into account.
Completions and expenditures are modelled as distributed lags on starts. The stock of existing houses is included in the residential construction expenditure equation to capture the effects of additions and alterations to existing residences plus commissions on the sale of existing homes.
3.6.7 MTFM
The MTFM housing sector treats single detached and multiple unit housing separately. Single unit housing is assumed to be owner occupied and multiple unit largely rental.
The key price equation is for Multiple Listing Service housing (PHMLS). It is determined by equating stock demand and supply for housing. Its form is:
PHMLS/PCPI * (.05 + RHPTR + RMCM/100 * IHLVES + RL10IND/100 * (1-IHLVES)) + PHIUR/PCPI
= A0 + A1 * YPERM/HP15 + A2 * KHS (-1)/HP15 + (JW(J1D(PHMLS(-1)*4)/PCPI
where PCPI is the CPI, .05 is the depreciation rate, RMCM is the conventional mortgage rate, IHLVES is the loan to value ratio, RL10IND is the McLeod, Young, Weir 10 industrial bond rate, PHIUR is the cost of insurance, utilities and
repairs, YPERM is permanent income, HP15 is the population
repairs, YPERM is permanent income, HP15 is the population